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I'm always having trouble talking about my mathematics in spoken German. For instance:

ℤ/nℤ ("the cyclic group "z over n z" or "z mod n z")

(ℤ/pℤ)× (the group non-zero elements of "z over p z")

And a more complex example related to field theory:

(ℤ/2ℤ)[T]/(T³+T+1) ("z mod two-z t – over t cubed plus t plus one", I guess..)

It would be even better if there was a glossary of some kind, telling me how to talk about these things. Still, my question: how do I talk about groups in spoken German?

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@MartyGreen: Would be nice to explain a bit more clearly, if that's how you leave comment everywhere then you will have trouble being understood in any website! –  user508 Nov 13 '11 at 9:59
Stefano, I didn't mean to criticize your English! I was answering you as though you were a native English speaker, and I was indeed criticizing the way you talked about mathematics. I am also a mathematician and it drives me crazy the way we use specialized jargon to talk about concepts that really should be spoken of in a more descriptive way. It's a problem I think we need to address in whatever language we are speaking. I'm sorry if I criticized you as an Italian who is doing a very good job of speaking English (much better than my Italian) because that was not myu intention. –  Marty Green Nov 13 '11 at 13:52
@MartyGreen I don't think you should have expressed your critique in this unhelpful form. Someone with an Italian name is a student in Germany where he learns mathematical terms in a non-native language. It would have been very useful if you had proposed some concrete ways of expressing things differently instead of just complaining about it. I agree that people often mistakenly blame the language barrier for a basic communication problem, but if you think it needs to be addressed, please actually address it. Write an English answer about the underlying problem, someone can then translate. –  Phira Nov 13 '11 at 17:05
@StefanoPalazzo You can learn much more by asking about whole sentences instead of isolated symbols. –  Phira Nov 13 '11 at 17:07
@Gigili "As always" = as always in compilations of mathematical language. I am quite frustrated with this myself. It is not enough to know a single phrase for each object to teach or give a good talk in another language. Sorry for the possible negative interpretation. I meant it when I said that it is a good link. –  Phira Nov 14 '11 at 6:43
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1 Answer

I would say:

Z modulo n.

In most contexts it will be unnecessary to mention Z here.

Die multiplikative Gruppe modulo p.

Die Polynome (mit Koeffizienten) modulo 2 in der Variable T modulo (dem Polynom) T hoch 3 plus T plus 1.

Note that one never says "T drei" for "T hoch drei" in German, but one can also say "T zur dritten".

Now, if I would have to dictate this stuff, I would say something like

Z modulo n Z.

Z modulo p Z, das ganze in Klammern, hoch dem Kreuzchen für die multiplikative Gruppe.

Z modulo 2 Z in Klammern von in eckigen Klammern T modulo in runden Klammern T hoch 3 plus T plus 1.

While no one speaks like this in a talk or a lecture (well, or no one should), it is important to know because it can be used in case of misunderstandings to point out that someone overlooked a parenthesis.

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Excellent stuff, this is pretty much what I was looking for. –  Stefano Palazzo Nov 13 '11 at 17:06
+1 for "T hoch drei". –  user508 Nov 13 '11 at 19:43
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